Importance of multidimensional latent subspaces
We remark again the importance of allowing subspaces with dimension \(d>1\) , which is a key point distinguishing our approach from current methods like [1]}, [2]}. We show a qualitative result of interpolation on disentangled subspaces on the FAUST dataset, increasing the dimensionality of the factorized latent space \(\mathcal {Z}\)  in Figure REF . We can see how, when a single factor represents a complex transformation class, having multidimensional disentangled subspaces allows to better capture the detailed behavior of the input data.
<FIGURE>